Instanton Sheaves - The Next Frontier in 3D Varieties
Explore the evolution of instanton sheaves on 3D varieties, from Atiyah-Ward correspondence to recent Bridgeland stability conditions, based on collaborative research.
Geometric Quantization of General Kähler Manifolds
Explore geometric quantization on Kähler manifolds, examining compatible constructions of function quantization, Hilbert space structure, and Kähler structure dependence in symplectic manifolds.
Asymptotics in Hitchin's Moduli Space
Explores asymptotic behavior in Hitchin's moduli space, comparing different notions of ideal points at infinity and examining the extension of the nonabelian Hodge correspondence between partial compactifications.
Constructing Polylogarithms on Higher-Genus Riemann Surfaces
Generalization of elliptic polylogarithms to higher-genus Riemann surfaces, exploring homotopy-invariant iterated integrals, modular tensors, and connections to Enriquez-Zerbini polylogarithms and Fay identities.
Prequantization of a Non-Exact Courant Algebroid
Explore advanced mathematical concepts in geometric structures, focusing on prequantization techniques for non-exact Courant algebroids in this in-depth lecture by Gavin Hurd.
Homological Mirror Symmetry - Recent Developments and Future Directions
Survey of recent developments in Homological Mirror Symmetry, exploring new results and future directions in this mathematical field. Honors Jeffrey Fuqua's contributions to the subject.
Homological Mirror Symmetry: Recent Developments and Future Directions
Explore recent advancements in Homological Mirror Symmetry, surveying new results and opening avenues for future development and collaboration in this transformative field of mathematics.
Algebraic Geometry in the Spectral Theory of Discrete Periodic Operators
Explore the intersection of algebraic geometry and spectral theory, focusing on discrete periodic operators and their applications in mathematical physics and analysis.
What is Symplectic Geometry?
Explore symplectic geometry fundamentals in this engaging lecture, covering key concepts, applications, and recent developments in this fascinating mathematical field.
Scaling Exponents in Stationary Random Graphs
Explore scaling exponents in stationary random graphs, examining relationships between fractal dimension, walk dimension, resistance, spectral dimension, and extremal growth in statistical physics.
Sharp Threshold for Rigidity of Random Graphs
Explore the evolution of random graphs and discover key moments when they become rigid and globally rigid, with implications for vertex embedding and distance preservation.
Cohomology Rings of Character Varieties
Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.
Hodge Theory for Poisson Varieties and Nonperturbative Quantization
Explore Hodge theory for Poisson varieties and nonperturbative quantization, focusing on K-theory and mixed Hodge structures to simplify complex calculations in deformation quantization.
An Overview on Closed G2-Structures
Overview of closed G_2-structures on 7-manifolds, exploring their definition, examples, and applications in holonomy G_2-metrics. Discusses Hitchin flow equations and the Laplacian G_2-flow in compact settings.
Calabi Problem in Generalized Kahler Geometry
Explores generalized Kahler structures, their connection to Kahler manifolds with holomorphic Poisson structures, and presents an approach to the Calabi problem in this context, with focus on toric complex Poisson varieties.
Calabi-Yau Theory in Generalized Kahler Geometry
Explore Calabi-Yau theory's extension to generalized Kahler geometry, examining connections to supergravity and geometric flow approaches for constructing solutions.
Commuting Pairs of Generalized Structures, Para-Hyper-Hermitian and Born Geometry
Explore generalized structures on manifolds, focusing on commuting pairs and their integrability. Delve into para-hyper-Hermitian and Born geometry within this context.
Double Groupoids and Generalized Kahler Structures
Explore double groupoids and generalized Kahler structures, focusing on holomorphic symplectic groupoids and their role in describing generalized Kahler metrics using a single real scalar function.
Future of Hitchin Mathematics - Round Table Discussion
Experts discuss advancements and future directions in Hitchin mathematics, exploring its impact on various mathematical fields and potential applications.
Components of Higgs Bundle Moduli Spaces - A Legacy of Hitchin's Ideas
Explore Higgs bundle moduli spaces, their components, and the lasting impact of Hitchin's groundbreaking ideas in this mathematical lecture by Steven Bradlow.
Variations on a Theme of Hitchin's System
Explores recent developments in Hitchin's system, including connections to SCFTs, extensions to integrable systems, geometry of the base, and links to the Deligne-Simpson problem.